# Uncertainty principle in Quantum mechanics

The Uncertainty principle says that "△x△p>h/2"; we cannot precisely obtain both position $x$ and momentum $p$ simultaneously.

Is this because the uncertainty is the natural characteristic or it is because we do not know additional values? (ex. like additional 11 dimensions in superstring theory.)

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It is an intrinsic property of our universe. There were some alternative interpretations, like the "hidden variables" (there are a swarm of deterministic random things going on that we don't know or cannot know about that cause the quantum randomness) but they have been experimentally disproven (Bell's theorem).

You have a nice list of the experiments here.

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"△x△p>h/2" is a simple consequence of the fundamental principle of using wavefunctions ("Amplitudes") to determine the probability of finding a particle.

A plane wave is evenly spread over all space and is the eigenfunction of one precisely known value of p.

In order to get anything other than such complete indeterminacy of position x, one must add several plane waves with different p, forming a wave packet which tails out at the spacial extremes and becomes more and more localised at one value of x, the more different p are added to the superposition.

In the limit you get an infinitely narrow wave packet (Dirac impulse), which is the eigenfunction of a precisely known value of x, which contains all possible p values (p is completely indeterminate).

Reality always lies in between these two extreme situations, and △x△p>h/2 follows from a Fourier analysis of the wave superposition (see e.g. Schiff: Quantum Mechanics).

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